Part A. Solve the equation for x showing all steps for credit: ax - 5 = 18
To solve this equation for x, we need to isolate the variable x on one side of the equation.
Step 1: Add 5 to both sides of the equation:
(ax - 5) + 5 = 18 + 5
ax = 23
Step 2: Divide both sides of the equation by a:
(ax)/a = 23/a
x = 23/a
Therefore, the solution for the equation is x = 23/a.
Part B. Solve the inequality for x showing all steps for credit: ax - 5 > 18
To solve this inequality for x, we need to isolate the variable x on one side of the inequality sign.
Step 1: Add 5 to both sides of the inequality:
(ax - 5) + 5 > 18 + 5
ax > 23
Step 2: Divide both sides of the inequality by a:
(ax)/a > 23/a
x > 23/a
Therefore, the solution for the inequality is x > 23/a.
Part C: State the difference between an equation and an inequality regarding solving steps and solutions
The main difference between an equation and an inequality is that an equation represents a statement of equality, whereas an inequality represents a statement of inequality.
When solving equations, the goal is to find a specific value that makes the equation true. The solving steps involve performing arithmetic operations to isolate the variable and determine the value that satisfies the equation.
On the other hand, when solving inequalities, the goal is to find a range of values that satisfy the inequality statement. The solving steps involve performing arithmetic operations to isolate the variable and determine the range of values that make the inequality true.
Therefore, the solutions for equations are typically specific values, while the solutions for inequalities are ranges of values.
Part A. Solve the equation for x showing all steps for credit: ax- 5 = 18
Part B. Solve the inequality for x showing all steps for credit: ax - 5 > 18
Part C: State the difference between an equation and an inequality regarding solving steps and solutions
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